Abstract
This note deals with a question on partial differential equations that has however several connections with infinite dimensional dynamical systems. The present state of knowledge on it is only very limited.
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References
B. Birnir, H. McKean, A. Weinstein: Nonexistence of breathers; private communication of draft 1990, publication being prepared.
J. P. Boyd: A numerical calculation of a weakly non-local solitary wave: the φ 4 breather, Nonlinearity 3 (1990), 177–195.
W. Craig, C.E. Wayne: Newton’s Method and Periodic Solutions of Nonlinear Wave Equations, preprint 1991.
A. Delshams, M.T. Martinez-Seara: An Asymptotic Expression for the Splitting of Separatrices of the Rapidly Forced Pendulum, to appear in Comm. Math. Phys.
V. M. Eleonskii, N. E. Kulagin, N. S. Novozhilova, V. P. Zilin: Asymptotic Expansions and Qualitative Analysis of Finite-Dimensional Models in Nonlinear Field Theory, Teor. i Mat. Fizika, 60,3 (1984), 395–403.
P. Holmes, J. Marsden, J. Scheurle: Exponentially Small Splittings of Separatrices with Applications to KAM Theory and Degenerate Bifurcations, Contemp. Math. 81 (1988), 213–244.
S. Kichenassamy: Breather Solutions of the Nonlinear Wave Equation, Comm. Pure Appl. Math. 44 (1991), 789–818.
V. F. Lazutkin, I. G. Schachmannski, M. B. Tabanov: Splitting of Separatrices for Standard and Semistandard Mappings, Physica D 40 (1989), 235–248.
D. W. McLaughlin, A. C. Scott: Perturbation analysis of fluxon dynamics, Physical Review A, 18, 4 (1978), 1652–1680.
J. Scheurle: Splitting of Separatrices and Chaos, Lect. in Appl. Math. 26 (1990), 561–571.
H. Segur, M. D. Kruskal: Nonexistence of Small Amplitude Breather Solutions in φ 4 Theory, Phys. Review Letters, 58 (1987), 747–750.
I.M. Sigal: Non-linear Wave and Schrödinger Equations I., Instability of Periodic and Quasiperiodic Solutions, preprint 1991.
A. Weinstein: Periodic Nonlinear Waves on a Half-Line, Commun. Math. Phys. 99 (1985), 385–388;
A. Weinstein: Periodic Nonlinear Waves on a Half-Line, Commun. Math. Phys. erratum 107 (1986), 177.
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Denzler, J. (1994). Nonpersistence of Breather Solutions under Perturbation of the Sine-Gordon Equation. In: Kuksin, S., Lazutkin, V., Pöschel, J. (eds) Seminar on Dynamical Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 12. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7515-8_16
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DOI: https://doi.org/10.1007/978-3-0348-7515-8_16
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